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Algebra

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Four positive integers A, B, C and D have a sum of 36. If A + 2 = B - 2 = C + 2 = D - 2,  what is the value of the product ABCD?

May 10, 2022

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$$\begin{array}{cc} &A + 2 = C + 2\\ \implies & A = C \end{array}$$

$$\begin{array}{cc} &B - 2 = D - 2\\ \implies & B = D \end{array}$$

$$\begin{array}{cc} &A + 2 = B - 2\\ \implies & B = A + 4 \end{array}$$

$$\begin{cases} A = C\\ B = D = A + 4 \end{cases}$$

Since A + B + C + D = 36 and with the above system of equation,

$$A + (A + 4) + A + (A + 4) = 36$$

Now you can solve for the value of A. If you know the value of A, you know the values of B, C, D. Then you will be able to find the product ABCD.

May 10, 2022